Equation 677 Database

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Magma 97b1a8b741a0…

magma 97b1a8b741a0
Size
705
Isomorphism class hash
97b1a8b741a0c0299cf3432037ebec28ab6ff07141deb59c6f907a8b2b53b0a2
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 704) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-03 19:20:02
Display reorder
660,101,326,531,221,343,102,344,327,532,222,100,345,325,533,220,104,322,342,530,224,105,323,340,528,225,103,324,341,529,223,107,317,349,537,227,108,318,350,538,228,106,316,351,539,226,320,110,348,536,230,321,111,346,534,231,319,109,347,535,229,668,666,671,661,165,519,543,205,379,163,380,520,544,206,164,381,521,545,207,161,518,378,542,204,162,516,376,540,202,160,517,377,541,203,171,525,385,549,196,169,526,386,550,197,170,527,387,551,198,524,167,384,548,199,522,168,382,546,200,523,166,383,547,201,689,685,687,686,12,31,75,555,251,13,252,35,73,556,14,250,28,74,557,15,18,254,71,554,16,21,255,72,552,17,24,253,70,553,10,32,249,66,561,11,34,247,64,562,9,29,248,65,563,20,6,245,69,560,23,7,246,67,558,26,8,244,68,559,672,669,662,663,131,88,391,595,77,132,78,89,392,596,130,76,90,393,597,134,91,80,390,594,135,92,81,388,592,133,93,79,389,593,129,94,83,397,601,127,95,84,398,602,128,96,82,399,603,97,125,86,396,600,98,126,87,394,598,99,124,85,395,599,675,683,681,673,41,192,571,495,471,39,472,190,572,496,40,473,191,573,497,37,195,470,570,494,38,193,468,568,492,36,194,469,569,493,47,187,477,577,501,45,188,478,578,502,46,189,479,579,503,186,43,476,576,500,184,44,474,574,498,185,42,475,575,499,670,667,664,665,328,117,238,451,507,329,508,115,239,452,330,509,116,240,453,331,113,506,241,450,332,114,504,242,448,333,112,505,243,449,334,123,513,236,457,335,121,514,237,458,336,122,515,235,459,119,337,512,232,456,120,338,510,233,454,118,339,511,234,455,695,696,693,697,48,463,63,467,567,49,631,630,629,628,50,635,632,634,633,51,464,564,62,462,52,465,565,60,460,53,466,566,61,461,54,649,651,650,648,55,653,655,654,652,56,656,659,658,657,644,57,647,646,645,637,58,639,638,636,641,59,643,642,640,703,702,701,704,179,439,611,610,139,180,140,440,613,612,178,141,441,614,615,182,438,138,608,609,183,436,136,604,605,181,437,137,606,607,177,445,145,623,622,175,446,146,624,625,176,447,147,626,627,444,173,144,620,621,442,174,142,617,616,443,172,143,618,619,699,700,694,698,310,355,427,412,218,311,219,356,428,413,312,217,357,429,414,313,354,214,426,415,314,352,215,424,416,315,353,216,425,417,308,361,209,433,418,309,362,210,434,419,307,363,208,435,420,360,304,212,432,421,358,305,213,430,422,359,306,211,431,423,677,680,674,684,364,155,403,483,583,365,584,156,404,484,366,585,154,405,485,367,158,582,402,482,368,159,580,400,480,369,157,581,401,481,370,153,589,409,489,371,151,590,410,490,372,152,591,411,491,149,373,588,408,488,150,374,586,406,486,148,375,587,407,487,676,679,678,682,33,256,281,272,292,27,293,257,282,273,30,294,258,280,271,22,259,295,284,268,25,260,296,285,269,19,261,297,283,270,3,262,298,287,278,4,263,299,288,279,5,264,300,286,277,265,2,301,290,274,266,1,302,291,275,267,0,303,289,276,688,690,692,691 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 705 = 1 + 11*64, from a common submagma at infinity. C(E, M, k, B) adjoins a submagma M (m elements) of a model E to every group of a transversal design TD(k, g), g = |E| - m, so that every enlarged group is a copy of E and all of them share M; every block carries B, a model of order k in which x*x = x. Two elements of M multiply in M; an element of M or of group i with one of group i, in group i's copy of E; elements of different groups, in their block. It satisfies Equation 677 whenever E and B do. This magma is C(E, M, 11, B) with E = magma#9dc1b7560e7dd8c4d9175d590a741d2999f3578c3e161e058f60df88b07e0ac9, M = {60} in E, B = magma#ca58a4a9ddeee171fc40b5c556a5095e4a2c63eee13557dcdf190986f06d14c3. Labels: 0..m-1 are M, in increasing order of their labels in E; m + g*i + c (i < k, c < g) is point c of group i, which plays the c-th element of E outside M, in increasing order. A block's point in group i plays element i of B. TD(11, 64): MacNeish's product over GF(64); GF(64) = F_2[x]/(x^6 + x + 1); GF(p^r) = F_p[x]/(f) labels c_0 + c_1 x + ... as c_0 + c_1 p + ..., and point c of a group is the c-th element of the product in lexicographic order. Block (a, b), a and b in the product, meets group i in the point whose coordinate in each field is a + s_i b, s_i the element of that field labelled i, or b when the field has exactly i elements. Equation 255: satisfied. Idempotent elements: 45.

last edited by qawbecrdtey at 2026-10-03 19:20:03 · history